In contemporary power grids for transmission and/or distribution of electrical power, it becomes increasingly complex to control the voltage of the various buses of the power grid. This is at least partially due to the increase of renewable power supply, which leads to faster power flow variations and reverse power flow from distribution grids to transmission grids.
Usually, a voltage control is to fulfill several requirements. First, the voltage of PQ buses (e.g., buses where the voltage cannot be controlled directly) may be within predetermined voltage limits Examples for PQ buses are load buses or buses with renewable power supply. Second, the voltage of PV buses (e.g., buses where the voltage level can be controlled directly) may be close to a nominal voltage value. Examples for PV buses are generator buses with conventional generators or buses with on-load tap changer (OLTC) transformers, reactive power compensators, flexible AC transmission systems (FACTS), or DC power grid terminals. These requirements may be fulfilled even in case of fast power variations of, for example, a renewable power supply. Hence, the voltage control may allow for a fast re-optimization after significant power flow variations, even for large power grids.
Known methods for voltage control in a power grid include methods based on numerically solving a set of nonlinear power flow equations, which combine values for active powers, reactive powers, voltage amplitudes and phase angles of the PV buses and the PQ buses of the power grid. It is known to solve these power flow equations for the voltage amplitudes at the PQ buses by inputting the values for the active and reactive power supply and demand at the PQ buses and the active power supply and demand and voltage amplitude at the PV buses. These input values are measured or estimated (e.g., based on predetermined load profiles). According to known methods, the optimal voltage levels at the PV buses are not determined directly but rather by an iterative solution of the power flow equations for different voltage levels. This often implies time consuming calculations. The dependence on estimated or varying values for the active and reactive power supply and demand leads to a significant increase of numerical complexity.